Algorithms for the analysis and identification of non-linear delay systems described by a Hammerstein model, which consists of a single-value non-linearity followed by a linear time-delayed plant, are presented. By using the finite-dimensional block-pulse expansion, the solution of a Hammerstein model non-linear dynamic system with time delay is reduced to the solution of a set of linear algebraic equations. In addition, through the block-pulse expansions of the measured input-output data, parameters of both the linear time-delayed plant and the polynomial approximation of the non-linear gain are estimated using the least-squares method. Examples are given to illustrate the utility of this method.